Idempotent Matrix

1. The problem statement, all variables and given/known data
A martix A is said to idempotent if A²=A prove the following:

a) If A is idempotent then I-A is also idempotent
b) If A is idempotent and invertible then A=I
c) If A is idempotent then I-2A is invertible.Find (I-2A)-1 in terms of A
d)Give an example of a 2x2 idempotent matrix A such that A is not the zero or the identity matrix